Optimal. Leaf size=12 \[ -\frac{2 x}{\sqrt{x^3+x}} \]
[Out]
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Rubi [A] time = 0.111015, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{2 x}{\sqrt{x^3+x}} \]
Antiderivative was successfully verified.
[In] Int[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^3]),x]
[Out]
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Rubi in Sympy [A] time = 12.4373, size = 15, normalized size = 1.25 \[ - \frac{2 \sqrt{x^{3} + x}}{x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-1)/(x**2+1)/(x**3+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0118042, size = 12, normalized size = 1. \[ -\frac{2 x}{\sqrt{x^3+x}} \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^3]),x]
[Out]
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Maple [A] time = 0.006, size = 11, normalized size = 0.9 \[ -2\,{\frac{x}{\sqrt{{x}^{3}+x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} - 1}{\sqrt{x^{3} + x}{\left (x^{2} + 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(sqrt(x^3 + x)*(x^2 + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270438, size = 22, normalized size = 1.83 \[ -\frac{2 \, \sqrt{x^{3} + x}}{x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(sqrt(x^3 + x)*(x^2 + 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (x - 1\right ) \left (x + 1\right )}{\sqrt{x \left (x^{2} + 1\right )} \left (x^{2} + 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-1)/(x**2+1)/(x**3+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} - 1}{\sqrt{x^{3} + x}{\left (x^{2} + 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(sqrt(x^3 + x)*(x^2 + 1)),x, algorithm="giac")
[Out]